Question

solve for #3

M ICH I Water for tetrachloroethene and led hloroethane assuming water solubilities of 150 and 8 mg/L, respectively. Also, sketch each compound (20 pts) Hint: ToXo = YwXw for pure organic = 1 3. (a) What is the pressure exerted by 24.0g of methane in a 5.00-L vessel at 0°C? (b) Find the density of methane at 20°C and 0.967 bar. (10 pts) Hint: (b) n = mole fraction = (m/M); m = mass and M: molecular weight

Answer 1

3) a)

Given : 1) Mass of methane ( m) = 24.0 g

2) volume of vessel = 5.00 L

3) temperature of gas = 0 ⁰ C = 273.15 K

We have relation , P V = n R T

where, P is a pressure of a gas, V is a volume of a gas, n is no. of moles of gas, R is a gas constant and T is temperature of gas.

$\therefore$ P = n R T / V

We know that, no. of moles = Mass / molar mass

Molar mass of CH 4 = 12.01 + ( 4 $\times$ 1.0079 ) = 16.04 g/ mol

Hence, no. of moles of methane gas = 24.0 g /16.04 g/mol = 1.496 mol

$\therefore$ Pressure exerted by methane gas = 1.496 mol $\times$ 0.082057 L atm mol ^-1 K ^-1$\times$ 273.15 K / 5.00 L

Pressure exerted by methane gas = 6.706 atm

ANSWER : Pressure exerted by methane gas = 6.71 atm

b)

We have relation, P V = n R T

But n = mass ( m ) / Molar mass (M)

$\therefore$ P V = (m / M ) R T

On rearranging above equation , we get

P M = (m / V ) R T

$\therefore$ P M = d R T

$\therefore$ density of gas = P M / R T

Given : Temperature = 20 + 273 .15 = 293.15 K

Pressure of gas = 0.967 bar = 0.9543 atm

Molar mass of methane gas = 16.04 g /mol

$\therefore$ density of methane gas = 0.9543 atm $\times$ 16.04 g /mol / 0.082057 L atm mol ^-1 K ^-1$\times$ 293.15 K

= 0.636 g / L

= 0.636 g / 1000 ml

= 0.000636 g / ml

ANSWER : Density of methane gas = 0.000636 g /ml